I have a 60 year old home that's styled in 1970's paneling. I am trying to remodel room by room as my family budget permits. The room that's going to be worked on next is part of a two story addition and needs to be ripped down to studs and blocks, re-insulated, drywalled, etc. One of the exterior walls is cinder blocks and 2 x 4's laid flat so I have 1-3/4" depth.

First, I thought exterior walls are typically 2 x 6. Next, if 2 x6's are the way I need to go then how do I do it?

Hi,
First off, I think the block walls are the load-bearing part of the structure, BUT the wood furring/studs may very well be tied into the ceiling joists in such a way that would require care if you remove them. You need a vapor barrier against the block walls. Sheet plastic will do; if you can take off the furring, you can build a 2x4 or 2x6 wall flat on the floor, affix the vapor barrier, and stand it up into place, then install full 3.5" or 5.5" batt insulation, and not lose too much more floor space.
If you want to leave the wood in place and add more to it, I suggest nailing 2x4's directly to the side of the furring, (use a string line to make a straight, flat wall) then spray-insulating with closed-cell foam, and there's your vapor barrier.
Casey

Install a layer of sheet plastic over the existing studs and block wall as a vapor barrier. It should be against the blocks without an airspace; you might need to use some spray adhesive to get it to stay there for the next step.

Then install 1-1/2" thick rigid foam board insulation cut to fit between the existing studs. So far, this is about R-5.75.

Install additional studs flat, but offset from the existing studs. This will provide thermal isolation so heat doesn't transfer from the wallboard to the stud to the next stud to the block wall. Insulate similarly between these studs. This will give you another R-5.75, for about R-11.5 insulation value.

If you want more insulation value, you can make the inner studs thicker either by building them up (adding 1/2" will allow you to use 2" foam board, with about R-10 value) or turning them "on edge" for an additional 3-1/2" which will net you an additional R-13 (with fiberglass batt insulation) for a total of almost R-19.

Even though the "R-value" might not be quite as much as a traditional 2x6 stud wall, the effective insulation value may actually be higher due to the thermal isolation of the staggered studs.